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puteri [66]
3 years ago
7

How much money would need to be deposited into an account earning 5.75% interest compounded annually in order for the accumulate

d value at the end of 25 years to be $85,000? a. $75,425.52 b. $59,130.43 c. $21,009.20 d. $20,258.70
Mathematics
2 answers:
Illusion [34]3 years ago
8 0

Answer:

c. $21009.20

Step-by-step explanation:

We are asked to find the principal amount of money that would be needed to deposited into an account earning 5.75% interest compounded annually in order for the accumulated value at the end of 25 years to be $85,000.

We will use compound interest formula to solve our given problem.

A=P(1+\frac{r}{n})^{nT}, where,

A = Final amount after T years,

P = Principal amount,

r = Interest rate in decimal form,

n = Number of times interest is compounded per year,

T = Time in years.

Let us convert our given interest rate in decimal form.

5.75\%=\frac{5.75}{100}=0.0575

Upon substituting our given values in compound interest formula we will get,

\$85,000=P(1+\frac{0.0575}{1})^{1*25}

\$85,000=P(1+0.0575)^{25}

\$85,000=P(1.0575)^{25}

\$85,000=P*4.0458464965061301

Let us divide both sides of our equation by 4.0458464965061301.

\frac{\$85,000}{4.0458464965061301}=\frac{P*4.0458464965061301}{4.0458464965061301}

\$21009.20044134235=P

Upon rounding our answer to nearest hundredth we will get,

P\approx \$21009.20

Therefore, an amount of $21009.20 should be deposited in the account and option 'c' is the correct choice.

mihalych1998 [28]3 years ago
5 0
I will assume you are using compound interest. 

let the amount invested be x 

x(1.0575)^25 = 85000 
<span>x = 85000/1.0575^25 = $21,009.20</span>
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